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Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative

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  • Zhijie Xiao

Abstract

We propose a new test for the null hypothesis that a time series is stationary around a deterministic trend. The test is valid under general conditions on stationarity. Asymptotic distributions of the test statistic are derived under both the null and the alternative hypothesis of a unit root. It is shown that the limiting distribution has the classical Kolmogoroff– Smirnoff form. Critical values for the null distribution are calculated. Consistency of the tests is proved. The tests provide a useful complement to the conventional unit root tests.

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  • Zhijie Xiao, 2001. "Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 87-105, January.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:1:p:87-105
    DOI: 10.1111/1467-9892.00213
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    Citations

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    Cited by:

    1. Amsler Christine & Schmidt Peter, 2012. "A Comparison of the Robustness of Several Tests of Short Memory to Autocorrelated Errors," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 56-66, August.
    2. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    3. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    4. A. M. Robert Taylor, 2005. "Fluctuation Tests for a Change in Persistence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 207-230, April.
    5. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2005. "Stationarity Tests Under Time-Varying Second Moments," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1112-1129, December.
    6. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    7. Wai-Sum Chan, 2006. "Outliers in Nonstationary Time Series," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 4(2), pages 75-83, July.
    8. Xiao, Zhijie, 2009. "Quantile cointegrating regression," Journal of Econometrics, Elsevier, vol. 150(2), pages 248-260, June.
    9. Xiao, Zhijie & Phillips, Peter C. B., 2002. "A CUSUM test for cointegration using regression residuals," Journal of Econometrics, Elsevier, vol. 108(1), pages 43-61, May.
    10. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.
    11. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    12. Ferrer-Pérez, H. & Ayuda, M.I. & Aznar, A., 2017. "A comparison of two modified stationarity tests. A Monte Carlo study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 28-36.
    13. Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers 08/2003, University of Verona, Department of Economics.
    14. Kapetanios, George, 2009. "Testing for strict stationarity in financial variables," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2346-2362, December.
    15. Lima, Luiz Renato & Xiao, Zhijie, 2007. "Do shocks last forever? Local persistency in economic time series," Journal of Macroeconomics, Elsevier, vol. 29(1), pages 103-122, March.
    16. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    17. Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 177-190, January.
    18. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    19. Shao, Xiaofeng & Wu, Wei Biao, 2007. "Local asymptotic powers of nonparametric and semiparametric tests for fractional integration," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 251-261, February.

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